From now on, we will focus on the study of this transition, specifically on the rules that relate the parameters
that characterize the first Kasner epoch \((\overline{c}, \overline{p})\) , which will be denoted with a bar,
with those that describe the second one \((\widetilde{c}, \widetilde{p})\) , and will be denoted with a tilde. The seminal idea to perform this analysis [1]} is to find the constants of motion of the system. Since they are conserved all along the evolution, these quantities shall be the same for both Kasner epochs. Therefore, one can write them in terms of the corresponding parameters
in each Kasner epoch, before (\(\alpha \rightarrow +\infty \) ) and after (\(\alpha \rightarrow -\infty \) ) the transition, and obtain the relations
\(\widetilde{c}=\widetilde{c}(\overline{c},\overline{p})\)  and \(\widetilde{p}=\widetilde{p}(\overline{c},\overline{p})\) . These relations will be known as the transition rules.
